Patrocinador

This paper is part of the work produced during the first author’s visit at the IEMath-Granada
and supported by it. The second author is supported by grant Proj. No. NRF-2011-220-C0002 from National
Research Foundation of Korea and by MCT-FEDER Grant MTM2010-18099.

Résumé

In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results concerning real hypersurfaces in complex hyperbolic space satisfying the above conditions are also provided.